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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
356b1db26f3ec5250e3ec042a21c98ad3f4735c4 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/foncteur/structure_sheaf.lean | 34f60a703df5473d52e86917b7ed05a87ce09877 | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,378 | lean | import tactic.ring
import tactic.ring_exp
import algebra.category.CommRing.basic
open category_theory
open functor
open CommRing
-- open algebra
-- open finsupp
universes v u
local notation ` Ring ` := CommRing.{u}
-- We start to define the affine line over ℤ ! This is a forget full foncteur... |
98518c7328529c25353266ae7d72b83279fa7549 | f3a5af2927397cf346ec0e24312bfff077f00425 | /src/mynat/le.lean | 28b5b8f8b4c5aee0e0f017c434d20853a00c6a4d | [
"Apache-2.0"
] | permissive | ImperialCollegeLondon/natural_number_game | 05c39e1586408cfb563d1a12e1085a90726ab655 | f29b6c2884299fc63fdfc81ae5d7daaa3219f9fd | refs/heads/master | 1,688,570,964,990 | 1,636,908,242,000 | 1,636,908,242,000 | 195,403,790 | 277 | 84 | Apache-2.0 | 1,694,547,955,000 | 1,562,328,792,000 | Lean | UTF-8 | Lean | false | false | 469 | lean | import mynat.mul
-- this is one of *three* routes to
-- canonically_ordered_comm_semiring
namespace mynat
def le (a b : mynat) := ∃ (c : mynat), b = a + c
-- Another choice is to define it recursively:
-- | le 0 _
-- | le (succ a) (succ b) = le ab
-- notation
instance : has_le mynat := ⟨mynat.le⟩
@[leakage] th... |
40ea397f8fbf5e853d7171c12a19b184d033d4d5 | 55c7fc2bf55d496ace18cd6f3376e12bb14c8cc5 | /src/data/nat/enat.lean | 95cd7fb8343297f33458d838bfcd64d2d575b584 | [
"Apache-2.0"
] | permissive | dupuisf/mathlib | 62de4ec6544bf3b79086afd27b6529acfaf2c1bb | 8582b06b0a5d06c33ee07d0bdf7c646cae22cf36 | refs/heads/master | 1,669,494,854,016 | 1,595,692,409,000 | 1,595,692,409,000 | 272,046,630 | 0 | 0 | Apache-2.0 | 1,592,066,143,000 | 1,592,066,142,000 | null | UTF-8 | Lean | false | false | 12,605 | lean | /-
Copyright (c) 2018 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
Natural numbers with infinity, represented as roption ℕ.
-/
import data.pfun
import tactic.norm_num
open roption
def enat : Type := roption ℕ
namespace enat
instance : ... |
0528d6b412b8889aa6ac15312b7def6e87fb68dd | 4b846d8dabdc64e7ea03552bad8f7fa74763fc67 | /library/init/data/int/basic.lean | d10c74c33c0d9447fe20e7d48da3eee31774d170 | [
"Apache-2.0"
] | permissive | pacchiano/lean | 9324b33f3ac3b5c5647285160f9f6ea8d0d767dc | fdadada3a970377a6df8afcd629a6f2eab6e84e8 | refs/heads/master | 1,611,357,380,399 | 1,489,870,101,000 | 1,489,870,101,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 13,759 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The integers, with addition, multiplication, and subtraction.
-/
prelude
import init.data.nat.lemmas init.meta.transfer
open nat
/- the type, coercions, and notation -/
... |
20bd81673dc874d4163f12a7ece7d9a2c03e8c53 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/1193a.lean | 4c1171444d429bdfca9522e2d5916788e69d78cc | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 343 | lean | inductive Foo (n : Nat) : Type
| nil : Foo n
| cons (s: Foo n): Foo n
namespace Foo
@[simp] def bar: {n: Nat} → Foo n → Foo n → Bool
| n+1, cons a, cons b => bar a b
| _, _, _ => true
example: bar (n:=n+1) nil nil = true := by
unfold bar
simp
example: bar (n:= Nat.succ n) nil nil = true := by
u... |
88767d1836df8b73c95bf9ce5dd3d94f4c4f0d60 | 48f4f349e1bb919d14ab7e5921d0cfe825f4c423 | /fabstract/Hales_T_et_al_Kepler_conj/fabstract.lean | e0392c3a7aa0f35600d1623c1e2bfee9a8ee21da | [] | no_license | thalesant/formalabstracts-2017 | fdf4ff90d30ab1dcb6d4cf16a068a997ea5ecc80 | c47181342c9e41954aa8d41f5049965b5f332bca | refs/heads/master | 1,584,610,453,925 | 1,528,277,508,000 | 1,528,277,508,000 | 136,299,625 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,458 | lean | import meta_data
...folklore.real_axiom
data.vector
namespace Hales_T_et_al_Kepler_conj
noncomputable theory
open classical nat set list real_axiom vector
-- cardinality of finite sets.
-- Surely this must exist somewhere. But where?
universe u
def set_of_list {α : Type u} : (list α) → set α
| [] y :... |
2674770e906250a839e045ce38e1d6342a938372 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/number_theory/liouville/basic.lean | e634ee31d3aec9c32e425055f7617f8429057fe8 | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 12,282 | lean | /-
Copyright (c) 2020 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Damiano Testa, Jujian Zhang
-/
import analysis.calculus.mean_value
import data.polynomial.denoms_clearable
import data.real.irrational
/-!
# Liouville's theorem
This file contains a pr... |
cd64277f6cea1245bdb019b0e0f28b0113208d4d | 675b8263050a5d74b89ceab381ac81ce70535688 | /src/ring_theory/algebra_tower.lean | 777fbad6ad51708c46e363fbb40bc097edacf9ad | [
"Apache-2.0"
] | permissive | vozor/mathlib | 5921f55235ff60c05f4a48a90d616ea167068adf | f7e728ad8a6ebf90291df2a4d2f9255a6576b529 | refs/heads/master | 1,675,607,702,231 | 1,609,023,279,000 | 1,609,023,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,229 | lean | /-
Copyright (c) 2020 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
-/
import algebra.invertible
import ring_theory.adjoin
import linear_algebra.basis
import algebra.algebra.basic
/-!
# Towers of algebras
We set up the basic theory of algebra t... |
760500ab22001a9c43e7d342a16d90863c0a5fae | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/algebra/group/inj_surj.lean | 7bf97969097decdaab823cadeb9ac3d4884182ee | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 14,269 | lean | /-
Copyright (c) 2020 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import algebra.group.defs
import logic.function.basic
/-!
# Lifting algebraic data classes along injective/surjective maps
This file provides definitions that are m... |
b4408ff07c41d3f13e4244b8b83bb48acf504cec | a4673261e60b025e2c8c825dfa4ab9108246c32e | /stage0/src/Lean/Compiler/IR/CompilerM.lean | 3905ede8ca56e10c8bdb7f30b5ff2206a0e13cb3 | [
"Apache-2.0"
] | permissive | jcommelin/lean4 | c02dec0cc32c4bccab009285475f265f17d73228 | 2909313475588cc20ac0436e55548a4502050d0a | refs/heads/master | 1,674,129,550,893 | 1,606,415,348,000 | 1,606,415,348,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,832 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Environment
import Lean.Compiler.IR.Basic
import Lean.Compiler.IR.Format
namespace Lean.IR
inductive LogEntry :=
| step (cls : Name) (decls ... |
816699b804aed4f4c0587ed5909d00691873dccf | 453dcd7c0d1ef170b0843a81d7d8caedc9741dce | /ring_theory/subring.lean | 8b5ae8eea3883365c4224a2fcd50b8a98bc19b3c | [
"Apache-2.0"
] | permissive | amswerdlow/mathlib | 9af77a1f08486d8fa059448ae2d97795bd12ec0c | 27f96e30b9c9bf518341705c99d641c38638dfd0 | refs/heads/master | 1,585,200,953,598 | 1,534,275,532,000 | 1,534,275,532,000 | 144,564,700 | 0 | 0 | null | 1,534,156,197,000 | 1,534,156,197,000 | null | UTF-8 | Lean | false | false | 1,965 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import group_theory.subgroup
import data.polynomial
import algebra.ring
local attribute [instance] classical.prop_decidable
universes u v
open group
variables {R ... |
eec07d7baf6115016a65466679f9e139c8dfe212 | e0f9ba56b7fedc16ef8697f6caeef5898b435143 | /src/measure_theory/integration.lean | f2950254d6ebce621e87f8afe1d508fb6e323798 | [
"Apache-2.0"
] | permissive | anrddh/mathlib | 6a374da53c7e3a35cb0298b0cd67824efef362b4 | a4266a01d2dcb10de19369307c986d038c7bb6a6 | refs/heads/master | 1,656,710,827,909 | 1,589,560,456,000 | 1,589,560,456,000 | 264,271,800 | 0 | 0 | Apache-2.0 | 1,589,568,062,000 | 1,589,568,061,000 | null | UTF-8 | Lean | false | false | 57,184 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Johannes Hölzl
Lebesgue integral on `ennreal`.
We define simple functions and show that each Borel measurable function on `ennreal` can be
approximated by a sequence ... |
82ed7beef6078ba1e748b3e895bccc55fa1f58d2 | c2d3fec70c4d83c328c648449c5f2b1c48e8c05c | /divides.lean | 00ba77acdad99aaab7b33045ccad10dabbe420f8 | [] | no_license | agro1986/lean-proofs | d603364212d46c30601da94660f4f0133a47d793 | a11b42ec47dbb347b66547d7e72e5154e13b6e85 | refs/heads/master | 1,598,977,963,373 | 1,572,882,333,000 | 1,572,882,333,000 | 219,005,217 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,204 | lean | variables {a b c: ℤ}
constant divides: ℤ → ℤ → Prop
axiom divides_expand: divides a b → ∃(d: ℤ), a * d = b
axiom divides_conclude: (∃(d: ℤ), a * d = b) → divides a b
theorem divides_trans (hab: divides a b) (hbc: divides b c):
divides a c :=
have h1: ∃m, a * m = b, from divides_expand hab,
have h2: ∃n, b * n = c... |
d37d74ca7420b0d9a589cdd63113fb6437763368 | a0e23cfdd129a671bf3154ee1a8a3a72bf4c7940 | /src/Lean/Elab/Match.lean | 5a4eedbd4e20ffcc3e65c04c77b9e2b0f981ff09 | [
"Apache-2.0"
] | permissive | WojciechKarpiel/lean4 | 7f89706b8e3c1f942b83a2c91a3a00b05da0e65b | f6e1314fa08293dea66a329e05b6c196a0189163 | refs/heads/master | 1,686,633,402,214 | 1,625,821,189,000 | 1,625,821,258,000 | 384,640,886 | 0 | 0 | Apache-2.0 | 1,625,903,617,000 | 1,625,903,026,000 | null | UTF-8 | Lean | false | false | 44,844 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Util.CollectFVars
import Lean.Meta.Match.MatchPatternAttr
import Lean.Meta.Match.Match
import Lean.Meta.SortLocalDecls
import Lean.Meta.Generali... |
02d4559dad9bbaa8e4b0e3dee9349bbe1c936081 | 8cb37a089cdb4af3af9d8bf1002b417e407a8e9e | /tests/lean/by_contradiction.lean | 5b05147c3d1c5a89505c29dab2be7124dec5d413 | [
"Apache-2.0"
] | permissive | kbuzzard/lean | ae3c3db4bb462d750dbf7419b28bafb3ec983ef7 | ed1788fd674bb8991acffc8fca585ec746711928 | refs/heads/master | 1,620,983,366,617 | 1,618,937,600,000 | 1,618,937,600,000 | 359,886,396 | 1 | 0 | Apache-2.0 | 1,618,936,987,000 | 1,618,936,987,000 | null | UTF-8 | Lean | false | false | 396 | lean | open tactic nat
example (a b : nat) : a ≠ b → ¬ a = b :=
by do
intros,
by_contradiction `H,
trace_state,
contradiction
#print "-------"
example (a b : nat) : ¬¬ a = b → a = b :=
by do
intros,
by_contradiction `H,
trace_state,
contradiction
#print "-------"
example (p q : Prop) : ¬¬ p → p :=
by do
... |
918bf27b0551e2e159d4de082f540cab35b22ce6 | 947b78d97130d56365ae2ec264df196ce769371a | /src/Std/Data/HashMap.lean | d32de5db7210e82a3c71f8da4847863737e8e9c1 | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,517 | lean | /-
Copyright (c) 2018 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
import Std.Data.AssocList
namespace Std
universes u v w
def HashMapBucket (α : Type u) (β : Type v) :=
{ b : Array (AssocList α β) // b.size > 0 }
def Hash... |
7a62b3edb534fb50dfd98325d3de84e49090848b | 947b78d97130d56365ae2ec264df196ce769371a | /tests/lean/run/typeclass_append.lean | 85635638a0e46b696e845508cbe3d43bfee7b69b | [
"Apache-2.0"
] | permissive | shyamalschandra/lean4 | 27044812be8698f0c79147615b1d5090b9f4b037 | 6e7a883b21eaf62831e8111b251dc9b18f40e604 | refs/heads/master | 1,671,417,126,371 | 1,601,859,995,000 | 1,601,860,020,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,467 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Selsam
Performance test to ensure quadratic blowup is avoided.
-/
new_frontend
class Append {α : Type} (xs₁ xs₂ : List α) (out : outParam $ List α) : Type :=
(u : Unit ... |
8918e104f58571aa3be6f256c0978271779c95d2 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/pfunctor/multivariate/W.lean | 23ac38bea5cfedb8a8496df0f0b7b16592c36d77 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 10,500 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Simon Hudon
-/
import data.pfunctor.multivariate.basic
/-!
# The W construction as a multivariate polynomial functor.
W types are well-founded tree-like structures. The... |
20a1b6f28d5e964063838cb314321e46642bd341 | 80d0f8071ea62262937ab36f5887a61735adea09 | /src/certigrad/rand.lean | 6a2896607c27d7850243a4ccc636d71dcc4d3c97 | [
"Apache-2.0"
] | permissive | wudcscheme/certigrad | 94805fa6a61f993c69a824429a103c9613a65a48 | c9a06e93f1ec58196d6d3b8563b29868d916727f | refs/heads/master | 1,679,386,475,077 | 1,551,651,022,000 | 1,551,651,022,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 10,289 | lean | /-
Copyright (c) 2017 Daniel Selsam. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Daniel Selsam
Stochastic operators.
-/
import .tensor .tfacts .tgrads .tcont .mvn
namespace certigrad
namespace rand
open list
def pdf_function (ishapes : list S) (oshape : S) : Type... |
a4bc6d300ad399da5aae61f1471deeaa95b885fb | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/e3.lean | a40f8011016705232a930646a8b045cfc5b730a2 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 433 | lean | prelude
definition Prop := Type.{0}
definition false := ∀x : Prop, x
#check false
noncomputable
theorem false.elim (C : Prop) (H : false) : C
:= H C
definition Eq {A : Type} (a b : A)
:= ∀ {P : A → Prop}, P a → P b
#check Eq
infix `=`:50 := Eq
noncomputable
theorem refl {A : Type} (a : A) : a = a
:= λ P H, H
non... |
344d50d45a972dd3b5866cf9c47f516d0c4e27f0 | a721fe7446524f18ba361625fc01033d9c8b7a78 | /src/principia/myint/int_pair.lean | f7145b558fac2305cf56919a3d7921ac905feda9 | [] | no_license | Sterrs/leaning | 8fd80d1f0a6117a220bb2e57ece639b9a63deadc | 3901cc953694b33adda86cb88ca30ba99594db31 | refs/heads/master | 1,627,023,822,744 | 1,616,515,221,000 | 1,616,515,221,000 | 245,512,190 | 2 | 0 | null | 1,616,429,050,000 | 1,583,527,118,000 | Lean | UTF-8 | Lean | false | false | 6,280 | lean | -- vim: ts=2 sw=0 sts=-1 et ai tw=70
-- Defining some operations on integers, thought of as pairs of
-- natural numbers (a, b), representing a - b.
-- Modelled heavily after frac from our myrat
import ..logic
import ..mynat.basic
import ..mynat.lt
namespace hidden
open mynat
namespace int_pair
-- the pair (a, b) r... |
0ef8405187ab81d48e2e4b4f70c29a4c096b2b4c | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /tests/lean/531.hlean | e867d51a07218930928b5af803d4b0228554c6e4 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 4,328 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: init.hit
Authors: Floris van Doorn
Declaration of hits
-/
structure diagram [class] :=
(Iob : Type)
(Ihom : Type)
(ob : Iob → Type)
(dom cod : Ihom → Iob)
(hom : Π(j : Ih... |
5618cb270fc97348edd795e124d5f6a07386a9fa | 4efff1f47634ff19e2f786deadd394270a59ecd2 | /src/category_theory/limits/shapes/constructions/limits_of_products_and_equalizers.lean | 24ccd296af9ec09f8bddd1f51a3b254ffc7e5ba2 | [
"Apache-2.0"
] | permissive | agjftucker/mathlib | d634cd0d5256b6325e3c55bb7fb2403548371707 | 87fe50de17b00af533f72a102d0adefe4a2285e8 | refs/heads/master | 1,625,378,131,941 | 1,599,166,526,000 | 1,599,166,526,000 | 160,748,509 | 0 | 0 | Apache-2.0 | 1,544,141,789,000 | 1,544,141,789,000 | null | UTF-8 | Lean | false | false | 4,708 | lean | /-
-- Copyright (c) 2017 Scott Morrison. All rights reserved.
-- Released under Apache 2.0 license as described in the file LICENSE.
-- Authors: Scott Morrison
-/
import category_theory.limits.shapes.equalizers
import category_theory.limits.shapes.finite_products
/-!
# Constructing limits from products and equalizers.... |
8f68476b956ebf32caf6346bea909c8ce2d71dce | 77c5b91fae1b966ddd1db969ba37b6f0e4901e88 | /src/data/equiv/mul_add_aut.lean | 39b3acbe4300cda86512262fb6c9ad1eb7ad8471 | [
"Apache-2.0"
] | permissive | dexmagic/mathlib | ff48eefc56e2412429b31d4fddd41a976eb287ce | 7a5d15a955a92a90e1d398b2281916b9c41270b2 | refs/heads/master | 1,693,481,322,046 | 1,633,360,193,000 | 1,633,360,193,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,190 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Callum Sutton, Yury Kudryashov
-/
import group_theory.perm.basic
/-!
# Multiplicative and additive group automorphisms
This file defines the automorphism group struct... |
e892d525b81bbd3c7cd3140cd26a51d55ddcbc0f | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/logic/hydra.lean | 7a6c92e116e0f16c0771ddfce198d8e9666b7cdb | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 6,610 | lean | /-
Copyright (c) 2022 Junyan Xu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Junyan Xu
-/
import data.finsupp.lex
import data.finsupp.multiset
import order.game_add
/-!
# Termination of a hydra game
This file deals with the following version of the hydra game: eac... |
dbb4e85ecc26c6ed18cad9883e9626a7f98c461d | 618003631150032a5676f229d13a079ac875ff77 | /archive/sensitivity.lean | 47cc930766dc1986d83f346d76cebb9e9b598f98 | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 15,511 | lean | /-
Copyright (c) 2019 Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert Y. Lewis, and
Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton, Johan Commelin, Jesse Han, Chris Hughes, Robert Y. Lewis, and Patrick Massot
-/
import tactic.f... |
34f8e37fa1a20705ca9738fc84b7e42a495f7b66 | c45b34bfd44d8607a2e8762c926e3cfaa7436201 | /uexp/src/uexp/rules/pushJoinThroughUnionOnLeft.lean | 56918029f598cf1118d05edf30d7c00fe5862500 | [
"BSD-2-Clause"
] | permissive | Shamrock-Frost/Cosette | b477c442c07e45082348a145f19ebb35a7f29392 | 24cbc4adebf627f13f5eac878f04ffa20d1209af | refs/heads/master | 1,619,721,304,969 | 1,526,082,841,000 | 1,526,082,841,000 | 121,695,605 | 1 | 0 | null | 1,518,737,210,000 | 1,518,737,210,000 | null | UTF-8 | Lean | false | false | 1,796 | lean | import ..sql
import ..tactics
import ..u_semiring
import ..extra_constants
import ..UDP
set_option profiler true
open Expr
open Proj
open Pred
open SQL
open tree
notation `int` := datatypes.int
theorem rule:
forall ( Γ scm_t scm_account scm_bonus scm_dept scm_emp: Schema) (rel_t: relation scm_t) (rel_account: r... |
39c22d29b8b96790912cb993c1e70721a995ff73 | d6124c8dbe5661dcc5b8c9da0a56fbf1f0480ad6 | /Papyrus/MemoryBufferRef.lean | a0d1691ea989feb60d332292993713f29e3caea9 | [
"Apache-2.0"
] | permissive | xubaiw/lean4-papyrus | c3fbbf8ba162eb5f210155ae4e20feb2d32c8182 | 02e82973a5badda26fc0f9fd15b3d37e2eb309e0 | refs/heads/master | 1,691,425,756,824 | 1,632,122,825,000 | 1,632,123,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 542 | lean | import Papyrus.FFI
namespace Papyrus
/--
An opaque type representing an LLVM
[MemoryBuffer](https://llvm.org/doxygen/classllvm_1_1MemoryBuffer.html).
-/
constant Llvm.MemoryBuffer : Type := Unit
/--
A reference to an external LLVM
[MemoryBuffer](https://llvm.org/doxygen/classllvm_1_1MemoryBuffer.html).
-/
de... |
624f5ec3a313b43532d6a4e0b639ad7b87394d38 | 4fa161becb8ce7378a709f5992a594764699e268 | /src/order/rel_classes.lean | 433687d194f94218723eb6f2eb3d33ae540c1f1e | [
"Apache-2.0"
] | permissive | laughinggas/mathlib | e4aa4565ae34e46e834434284cb26bd9d67bc373 | 86dcd5cda7a5017c8b3c8876c89a510a19d49aad | refs/heads/master | 1,669,496,232,688 | 1,592,831,995,000 | 1,592,831,995,000 | 274,155,979 | 0 | 0 | Apache-2.0 | 1,592,835,190,000 | 1,592,835,189,000 | null | UTF-8 | Lean | false | false | 16,933 | lean | /-
Copyright (c) 2020 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Mario Carneiro, Yury G. Kudryashov
-/
import tactic.simpa
import tactic.rcases
import tactic.lint.misc
import algebra.order
import order.basic
/-!
# Unbundled relation c... |
bb4fa93b7825f260161e4ac29520fb7de0e2d86e | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/ring_theory/fractional_ideal.lean | 94189405de0080fd16d0a279eb256484fd33d660 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 53,483 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen, Filippo A. E. Nuccio
-/
import algebra.big_operators.finprod
import ring_theory.integral_closure
import ring_theory.localization.integer
import ring_theory.localization.submo... |
b184478c676119740e9b639c04d7d98bc412c281 | 2c096fdfecf64e46ea7bc6ce5521f142b5926864 | /src/Lean/Parser/Extra.lean | daae855283a5d9e553ea971248934868875ab1d8 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | Kha/lean4 | 1005785d2c8797ae266a303968848e5f6ce2fe87 | b99e11346948023cd6c29d248cd8f3e3fb3474cf | refs/heads/master | 1,693,355,498,027 | 1,669,080,461,000 | 1,669,113,138,000 | 184,748,176 | 0 | 0 | Apache-2.0 | 1,665,995,520,000 | 1,556,884,930,000 | Lean | UTF-8 | Lean | false | false | 10,212 | lean | /-
Copyright (c) 2019 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura, Sebastian Ullrich
-/
import Lean.Parser.Extension
-- necessary for auto-generation
import Lean.PrettyPrinter.Parenthesizer
import Lean.PrettyPrinter.Formatter... |
3751cd25a620cb97fdc57ea59e15452c387215a9 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/monoidal/natural_transformation.lean | e6566fc826eb83e0e4901b33e6e574a1e0f47a92 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,775 | lean | /-
Copyright (c) 2020 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.monoidal.functor
import Mathlib.category_theory.full_subcategory
import Mat... |
b24daae955b350f3848031128728022cbe372630 | 75db7e3219bba2fbf41bf5b905f34fcb3c6ca3f2 | /hott/algebra/category/functor/basic.hlean | c7110b70798dd653184e1851522defd38671f3a4 | [
"Apache-2.0"
] | permissive | jroesch/lean | 30ef0860fa905d35b9ad6f76de1a4f65c9af6871 | 3de4ec1a6ce9a960feb2a48eeea8b53246fa34f2 | refs/heads/master | 1,586,090,835,348 | 1,455,142,203,000 | 1,455,142,277,000 | 51,536,958 | 1 | 0 | null | 1,455,215,811,000 | 1,455,215,811,000 | null | UTF-8 | Lean | false | false | 12,248 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Jakob von Raumer
-/
import ..iso types.pi
open function category eq prod prod.ops equiv is_equiv sigma sigma.ops is_trunc funext iso pi
structure functor (C D : ... |
6930245d6360e3adde565c061c744febf487ef3d | 5ae26df177f810c5006841e9c73dc56e01b978d7 | /src/topology/uniform_space/complete_separated.lean | 225ad7af2c66c3d35d73ee449592c28d17b18060 | [
"Apache-2.0"
] | permissive | ChrisHughes24/mathlib | 98322577c460bc6b1fe5c21f42ce33ad1c3e5558 | a2a867e827c2a6702beb9efc2b9282bd801d5f9a | refs/heads/master | 1,583,848,251,477 | 1,565,164,247,000 | 1,565,164,247,000 | 129,409,993 | 0 | 1 | Apache-2.0 | 1,565,164,817,000 | 1,523,628,059,000 | Lean | UTF-8 | Lean | false | false | 1,295 | lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
Theory of complete separated uniform spaces.
This file is for elementary lemmas that depend on both Cauchy filters and separation.
-/
import topology.uniform_spa... |
fc8b7ac1acc909a94acc596e298ca4f7e41d75b9 | 624f6f2ae8b3b1adc5f8f67a365c51d5126be45a | /stage0/src/Init/Data/Int/Basic.lean | 2de502f03ebb6c15f6c9569a1766285672e124c5 | [
"Apache-2.0"
] | permissive | mhuisi/lean4 | 28d35a4febc2e251c7f05492e13f3b05d6f9b7af | dda44bc47f3e5d024508060dac2bcb59fd12e4c0 | refs/heads/master | 1,621,225,489,283 | 1,585,142,689,000 | 1,585,142,689,000 | 250,590,438 | 0 | 2 | Apache-2.0 | 1,602,443,220,000 | 1,585,327,814,000 | C | UTF-8 | Lean | false | false | 4,589 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Leonardo de Moura
The integers, with addition, multiplication, and subtraction.
-/
prelude
import Init.Data.Nat.Basic
import Init.Data.List
import Init.Data.Repr
import ... |
dc6362c803c5d446154fdacc53787239bf11d5f7 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/prod.lean | 9ccfa0badfa8fa879d4b80d01f103c09ca238bc5 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 8,992 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import tactic.basic
/-!
# Extra facts about `prod`
This file defines `prod.swap : α × β → β × α` and proves various simple lemmas about `prod`.
-/
variables {α : T... |
32f247f5dff5825e1e75aa89a84f025045c54a1b | f00cc9c04d77f9621aa57d1406d35c522c3ff82c | /library/init/meta/transfer.lean | 8c9e591cf271064f838e7068848ad80b80e2cf18 | [
"Apache-2.0"
] | permissive | shonfeder/lean | 444c66a74676d74fb3ef682d88cd0f5c1bf928a5 | 24d5a1592d80cefe86552d96410c51bb07e6d411 | refs/heads/master | 1,619,338,440,905 | 1,512,842,340,000 | 1,512,842,340,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 7,437 | lean | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Johannes Hölzl (CMU)
-/
prelude
import init.meta.tactic init.meta.match_tactic init.relator init.meta.mk_dec_eq_instance
import init.data.list.instances
namespace transfer
open tactic ... |
660f88ef8d13a84c086bc914a03b6334015f4e56 | 4d2583807a5ac6caaffd3d7a5f646d61ca85d532 | /src/linear_algebra/clifford_algebra/basic.lean | 305529cecbaf5eec957abefeb8498a0df573a15e | [
"Apache-2.0"
] | permissive | AntoineChambert-Loir/mathlib | 64aabb896129885f12296a799818061bc90da1ff | 07be904260ab6e36a5769680b6012f03a4727134 | refs/heads/master | 1,693,187,631,771 | 1,636,719,886,000 | 1,636,719,886,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 12,274 | lean | /-
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Utensil Song
-/
import algebra.ring_quot
import linear_algebra.tensor_algebra
import linear_algebra.exterior_algebra
import linear_algebra.quadratic_form.basic
/-!
# Cliffo... |
2819e5eb38ba1d2a8cdf732a5eb35bf5974f27aa | 82e44445c70db0f03e30d7be725775f122d72f3e | /src/analysis/convex/extreme.lean | 5cf0df95d33c3adb70851768cfd80ba58288a55d | [
"Apache-2.0"
] | permissive | stjordanis/mathlib | 51e286d19140e3788ef2c470bc7b953e4991f0c9 | 2568d41bca08f5d6bf39d915434c8447e21f42ee | refs/heads/master | 1,631,748,053,501 | 1,627,938,886,000 | 1,627,938,886,000 | 228,728,358 | 0 | 0 | Apache-2.0 | 1,576,630,588,000 | 1,576,630,587,000 | null | UTF-8 | Lean | false | false | 8,757 | lean | /-
Copyright (c) 2021 Yaël Dillies, Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Bhavik Mehta
-/
import analysis.convex.basic
/-!
# Extreme sets
This file defines extreme sets and extreme points for sets in a real vector space.
An extre... |
feb1d875e400ac762d5e01a6b3f3160d1dd20726 | 57c233acf9386e610d99ed20ef139c5f97504ba3 | /src/data/part.lean | 658825cc73c10685d656f239cdb12adf55c5facb | [
"Apache-2.0"
] | permissive | robertylewis/mathlib | 3d16e3e6daf5ddde182473e03a1b601d2810952c | 1d13f5b932f5e40a8308e3840f96fc882fae01f0 | refs/heads/master | 1,651,379,945,369 | 1,644,276,960,000 | 1,644,276,960,000 | 98,875,504 | 0 | 0 | Apache-2.0 | 1,644,253,514,000 | 1,501,495,700,000 | Lean | UTF-8 | Lean | false | false | 16,831 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Jeremy Avigad, Simon Hudon
-/
import data.equiv.basic
import data.set.basic
/-!
# Partial values of a type
This file defines `part α`, the partial values of a type.
... |
111f96f81a4ede6d4cb8569955709f0d2e0b1290 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/group_theory/group_action/sub_mul_action/pointwise.lean | d09c82d90301956ad93fedcbc34faab2cb98ca7a | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 3,625 | lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import group_theory.group_action.sub_mul_action
/-!
# Pointwise monoid structures on sub_mul_action
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file... |
7eefc4bfb19df9e6f99ded80eb169586a7a10b0f | 46125763b4dbf50619e8846a1371029346f4c3db | /src/ring_theory/fractional_ideal.lean | ba0171abbe754b291c7b04da7bbbabe94899e47b | [
"Apache-2.0"
] | permissive | thjread/mathlib | a9d97612cedc2c3101060737233df15abcdb9eb1 | 7cffe2520a5518bba19227a107078d83fa725ddc | refs/heads/master | 1,615,637,696,376 | 1,583,953,063,000 | 1,583,953,063,000 | 246,680,271 | 0 | 0 | Apache-2.0 | 1,583,960,875,000 | 1,583,960,875,000 | null | UTF-8 | Lean | false | false | 14,253 | lean | /-
Copyright (c) 2020 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
Fractional ideals of an integral domain.
-/
import ring_theory.algebra_operations
import ring_theory.localization
/-!
# Fractional ideals
This file defines fractional ideal... |
0fd3dbd90db04ead1cf5633cf357f2d4bb30450c | 69d4931b605e11ca61881fc4f66db50a0a875e39 | /src/group_theory/specific_groups/cyclic.lean | a3ec18f191d0fd083470efa12d15e4332ffcdcdb | [
"Apache-2.0"
] | permissive | abentkamp/mathlib | d9a75d291ec09f4637b0f30cc3880ffb07549ee5 | 5360e476391508e092b5a1e5210bd0ed22dc0755 | refs/heads/master | 1,682,382,954,948 | 1,622,106,077,000 | 1,622,106,077,000 | 149,285,665 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 17,540 | lean | /-
Copyright (c) 2018 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl
-/
import group_theory.order_of_element
/-!
# Cyclic groups
A group `G` is called cyclic if there exists an element `g : G` such that every element of `G` is of
the f... |
289e7de4a1940a0774e2f1a5e242147b9eb1ad13 | 9028d228ac200bbefe3a711342514dd4e4458bff | /src/data/padics/hensel.lean | b5a4329d02c7b2987990e7dfd6a55b391a5c5a91 | [
"Apache-2.0"
] | permissive | mcncm/mathlib | 8d25099344d9d2bee62822cb9ed43aa3e09fa05e | fde3d78cadeec5ef827b16ae55664ef115e66f57 | refs/heads/master | 1,672,743,316,277 | 1,602,618,514,000 | 1,602,618,514,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 21,292 | lean | /-
Copyright (c) 2018 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis
-/
import data.padics.padic_integers
import topology.metric_space.cau_seq_filter
import analysis.specific_limits
import data.polynomial.identities
import topology.alge... |
fccecae969f2531941b5845cdab31f18ce96bc56 | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/eq15.lean | 90198cb42c472af0d27981aa9be879fd28fcc908 | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 460 | lean | import data.list
open list
set_option pp.implicit true
definition append : Π {A : Type}, list A → list A → list A
| append nil l := l
| append (h :: t) l := h :: (append t l)
theorem append_nil {A : Type} (l : list A) : append nil l = l :=
rfl
theorem append_cons {A : Type} (h : A) (t l : list A) : append (h :... |
48621f3fc4c59dd31e88942706683f8180ad99c8 | 3dc4623269159d02a444fe898d33e8c7e7e9461b | /.github/workflows/project_1_a_decrire/lean-scheme-submission/src/to_mathlib/localization/local_rings.lean | 4a95b977d58c4ffc2cdf94b20ab6f097ec064d3a | [] | no_license | Or7ando/lean | cc003e6c41048eae7c34aa6bada51c9e9add9e66 | d41169cf4e416a0d42092fb6bdc14131cee9dd15 | refs/heads/master | 1,650,600,589,722 | 1,587,262,906,000 | 1,587,262,906,000 | 255,387,160 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 3,914 | lean | /-
A ring with the localization property at a prime ideal is a local ring.
-/
import ring_theory.ideals
import ring_theory.localization
import to_mathlib.localization.localization_alt
universes u v
local attribute [instance] classical.prop_decidable
open localization_alt
variables {α : Type u} {β : Type v} [com... |
a14f83c47e1175ce38af41e4eeab30bac0fdd606 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/lean/run/split3.lean | 7a1da30984ed5dbd9fa580d9c390c5b172a1cc34 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 1,016 | lean | def g (xs ys : List Nat) : Nat :=
match xs, ys with
| [a, b], _ => Nat.succ (a+b)
| _, [b, c] => Nat.succ b
| _, _ => 1
example (a b : Bool) (x y z : Nat) (xs : List Nat) (h1 : (if a then x else y) = 0) (h2 : xs.head! = 0) : g [x] xs = 1 := by
simp [g]
repeat any_goals (split at *)
any_goals (first | d... |
1f078c03570a565eb61f480a6a651e92f7a4665d | f1b175e38ffc5cc1c7c5551a72d0dbaf70786f83 | /algebra/archimedean.lean | 272b00a20bb091f74af36c0ba834f6ee3a680995 | [
"Apache-2.0"
] | permissive | mjendrusch/mathlib | df3ae884dd5ce38c7edf452bcbfd3baf4e3a6214 | 5c209edb7eb616a26f64efe3500f2b1ba95b8d55 | refs/heads/master | 1,585,663,284,800 | 1,539,062,055,000 | 1,539,062,055,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 9,912 | lean | /-
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
Archimedean groups and fields.
-/
import algebra.group_power data.rat
local infix ` • ` := add_monoid.smul
variables {α : Type*}
class floor_ring (α) extends linear_... |
2eecfc713933ab5fe7d98a97b3d3da54e07437e4 | ac1c2a2f522b0fdf854095ba00f882ca849669e7 | /tests/lean/char_lits.lean | 2ea38d07fbc77430a3329fbf40ca4045d275fd32 | [
"Apache-2.0"
] | permissive | abliss/lean | b8b336abc8d50dbb0726dcff9dd16793c23bfbe1 | fb24cc99573c153f97a1951ee94bbbdda300b6be | refs/heads/master | 1,611,536,584,520 | 1,497,811,981,000 | 1,497,811,981,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 222 | lean | import system.io
open io
#check 'a'
#eval 'a'
#eval '\n'
#eval '\\'
variable [io.interface]
#eval put_str ("aaa".str '\\')
#eval put_str '\n'.to_string
#eval put_str $ string.singleton '\n'
#eval put_str ("aaa".str '\'')
|
abb20a93b88eb3d56a86add21fa688922e138e1b | e94d3f31e48d06d252ee7307fe71efe1d500f274 | /hott/types/pointed.hlean | 30026578dc40d899f0c7e051550323717e789d90 | [
"Apache-2.0"
] | permissive | GallagherCommaJack/lean | e4471240a069d82f97cb361d2bf1a029de3f4256 | 226f8bafeb9baaa5a2ac58000c83d6beb29991e2 | refs/heads/master | 1,610,725,100,482 | 1,459,194,829,000 | 1,459,195,377,000 | 55,377,224 | 0 | 0 | null | 1,459,731,701,000 | 1,459,731,700,000 | null | UTF-8 | Lean | false | false | 18,954 | hlean | /-
Copyright (c) 2014 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer, Floris van Doorn
Ported from Coq HoTT
-/
import arity .eq .bool .unit .sigma .nat.basic prop_trunc
open is_trunc eq prod sigma nat equiv option is_equiv bool unit... |
28ea5dd93df6abecc1ce43c0f582d7b7750782c8 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/Lean3Lib/init/data/prod.lean | 263414a8ca41e1654170d8155653159ee9138fa4 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 1,788 | lean | /-
Copyright (c) 2014 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura, Jeremy Avigad
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.logic
universes u v u₁ u₂ v₁ v₂
namespace Mathlib
@[simp] theorem prod.mk.eta {α : T... |
30d43a520a585b3604a7f62f7deedbe797b16fbf | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/analysis/normed_space/bounded_linear_maps.lean | cf2ee4b87f7f85461e623e56957a8d92c3f0ee09 | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 7,044 | lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
Continuous linear functions -- functions between normed vector spaces which are bounded and linear.
-/
import algebra.field
import analysis.normed_space... |
80e24adcd2bf970dc6b924d525bd1225c6e315d2 | d1bbf1801b3dcb214451d48214589f511061da63 | /src/data/fin.lean | b3d8c9d023805d553f1176afb5dfd817d06e9940 | [
"Apache-2.0"
] | permissive | cheraghchi/mathlib | 5c366f8c4f8e66973b60c37881889da8390cab86 | f29d1c3038422168fbbdb2526abf7c0ff13e86db | refs/heads/master | 1,676,577,831,283 | 1,610,894,638,000 | 1,610,894,638,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 50,731 | lean | /-
Copyright (c) 2017 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Robert Y. Lewis, Keeley Hoek
-/
import data.nat.cast
import tactic.localized
import order.rel_iso
/-!
# The finite type with `n` elements
`fin n` is the type whose elements are natu... |
92da3386b1daa0451084e76c3ddba4d2214b1437 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/1804b.lean | 76a2b3b0f3a8057373a8c3342e55bfd2b65ad3eb | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 652 | lean | namespace bla
private def foo (x : nat) : nat :=
match x with
| 0 := 1
| _ := 2
end
example (a : nat) (h : a = foo 0) : a = 1 :=
begin
simp [foo] at h,
guard_hyp h : a = 1,
exact h
end
example (a b : nat) (p : b = 0) (h : a = foo b) : a = 1 :=
begin
simp [foo] at h,
simp [p] at h,
simp [foo._match_1] at ... |
4f88c315ce9d01841b7d7da9fd5356be750901fc | 27a31d06bcfc7c5d379fd04a08a9f5ed3f5302d4 | /tests/lean/server/init_exit_worker.lean | cb4b46ba2df81b55030f0b30d2a34b4ec1c9df11 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | joehendrix/lean4 | 0d1486945f7ca9fe225070374338f4f7e74bab03 | 1221bdd3c7d5395baa451ce8fdd2c2f8a00cbc8f | refs/heads/master | 1,640,573,727,861 | 1,639,662,710,000 | 1,639,665,515,000 | 198,893,504 | 0 | 0 | Apache-2.0 | 1,564,084,645,000 | 1,564,084,644,000 | null | UTF-8 | Lean | false | false | 443 | lean | import Lean.Data.Lsp
open IO Lean Lsp
#eval (do
Ipc.runWith (←IO.appPath) #["--worker"] do
let hIn ← Ipc.stdin
hIn.write (←FS.readBinFile "init_vscode_1_47_2.log")
hIn.flush
hIn.write (←FS.readBinFile "open_empty.log")
hIn.flush
let diags ← Ipc.collectDiagnostics 1 "file:///empty" 1
asse... |
db1966dd850db0b723eeb86527ba7433ed6fa12d | 367134ba5a65885e863bdc4507601606690974c1 | /src/data/qpf/univariate/basic.lean | 5a1d67992efc24e6091940ff278c18270712c719 | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 21,834 | lean | /-
Copyright (c) 2018 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Jeremy Avigad
-/
import data.pfunctor.univariate
/-!
# Quotients of Polynomial Functors
We assume the following:
`P` : a polynomial functor
`W` : its W-type
`M` : its M-type
`F... |
932cf91ca8dffbda2bf85580d68eefcfec163aff | b7f22e51856f4989b970961f794f1c435f9b8f78 | /tests/lean/run/inf_tree.lean | 29f5605601f8420d38a8518bf6f4393d416725ba | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 1,502 | lean | import logic data.nat.basic
open nat
inductive inftree (A : Type) :=
| leaf : A → inftree A
| node : (nat → inftree A) → inftree A
namespace inftree
inductive dsub {A : Type} : inftree A → inftree A → Prop :=
intro : Π (f : nat → inftree A) (a : nat), dsub (f a) (node f)
definition dsub.node.acc {A : Type} (f ... |
3c5588c108029df3ed8255bb996c2672c8d67f92 | d1a52c3f208fa42c41df8278c3d280f075eb020c | /tests/lean/server/init_exit.lean | d5addb231a41cf799e229296864d327106dd5688 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | cipher1024/lean4 | 6e1f98bb58e7a92b28f5364eb38a14c8d0aae393 | 69114d3b50806264ef35b57394391c3e738a9822 | refs/heads/master | 1,642,227,983,603 | 1,642,011,696,000 | 1,642,011,696,000 | 228,607,691 | 0 | 0 | Apache-2.0 | 1,576,584,269,000 | 1,576,584,268,000 | null | UTF-8 | Lean | false | false | 559 | lean | import Lean.Data.Lsp
open IO Lean Lsp
def main : IO Unit := do
Ipc.runWith (←IO.appPath) #["--server"] do
let hIn ← Ipc.stdin
hIn.write (←FS.readBinFile "init_vscode_1_47_2.log")
hIn.flush
let initResp ← Ipc.readResponseAs 0 InitializeResult
Ipc.writeNotification ⟨"initialized", InitializedParams... |
9c8fd1db547f1c8fff73b91a8bc67616a6bbf0bb | 42610cc2e5db9c90269470365e6056df0122eaa0 | /library/data/pnat.lean | 4a328329d767830d8e1057ab5f18259a58b264f1 | [
"Apache-2.0"
] | permissive | tomsib2001/lean | 2ab59bfaebd24a62109f800dcf4a7139ebd73858 | eb639a7d53fb40175bea5c8da86b51d14bb91f76 | refs/heads/master | 1,586,128,387,740 | 1,468,968,950,000 | 1,468,968,950,000 | 61,027,234 | 0 | 0 | null | 1,465,813,585,000 | 1,465,813,585,000 | null | UTF-8 | Lean | false | false | 12,662 | lean | /-
Copyright (c) 2015 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Robert Y. Lewis
Basic facts about the positive natural numbers.
Developed primarily for use in the construction of ℝ. For the most part, the only theorems here
are those needed for t... |
9029f07dfca98d24c80990433273c10fe23a77ea | 4727251e0cd73359b15b664c3170e5d754078599 | /src/geometry/manifold/bump_function.lean | a3213d6934f697d90ca434d9bdc9044c80f7f80b | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 14,138 | lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import analysis.calculus.specific_functions
import geometry.manifold.cont_mdiff
/-!
# Smooth bump functions on a smooth manifold
In this file we define `smooth_bu... |
f58ed2e731664fab6875ae262df8b23c4c910698 | d406927ab5617694ec9ea7001f101b7c9e3d9702 | /src/algebraic_topology/dold_kan/normalized.lean | d7d0db4ea424c0f7c8b87e5db288d4cb3dac7074 | [
"Apache-2.0"
] | permissive | alreadydone/mathlib | dc0be621c6c8208c581f5170a8216c5ba6721927 | c982179ec21091d3e102d8a5d9f5fe06c8fafb73 | refs/heads/master | 1,685,523,275,196 | 1,670,184,141,000 | 1,670,184,141,000 | 287,574,545 | 0 | 0 | Apache-2.0 | 1,670,290,714,000 | 1,597,421,623,000 | Lean | UTF-8 | Lean | false | false | 5,558 | lean | /-
Copyright (c) 2022 Joël Riou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joël Riou
-/
import algebraic_topology.dold_kan.functor_n
/-!
# Comparison with the normalized Moore complex functor
TODO (@joelriou) continue adding the various files referenced below
... |
a77686c51101df8472952f393334a6930e03f6eb | 586535ff9853f5b85dc5fdeb5b78f1ad2d573a6e | /src/theorem.lean | a937f49b50ec25fac464cfa1350242d7779f8832 | [
"Apache-2.0"
] | permissive | Kha/rc-correctness | fede4ae228c5f04985cf332e718a5a433230b150 | be5a521f1b0528ccbc685619b265cd11ea854edf | refs/heads/master | 1,595,967,325,275 | 1,568,889,756,000 | 1,568,889,756,000 | 209,523,947 | 0 | 0 | Apache-2.0 | 1,568,888,337,000 | 1,568,888,336,000 | null | UTF-8 | Lean | false | false | 24,166 | lean | import compiler
import well_foundedness
namespace rc_correctness
open rc_correctness.expr
open rc_correctness.fn_body
open rc_correctness.ob_lin_type
open rc_correctness.lin_type
section FV_wf
open finset
open list
theorem FV_subset_finset_var {δ : const → fn} {β : const → var → ob_lin_type} {Γ Δ : finset var... |
2f6fabeb3328bed4986e5f780919aff77a5865e5 | 1a61aba1b67cddccce19532a9596efe44be4285f | /hott/algebra/category/nat_trans.hlean | 8a3a8d0b12d4cca1d3e06100c7666d92c641152b | [
"Apache-2.0"
] | permissive | eigengrau/lean | 07986a0f2548688c13ba36231f6cdbee82abf4c6 | f8a773be1112015e2d232661ce616d23f12874d0 | refs/heads/master | 1,610,939,198,566 | 1,441,352,386,000 | 1,441,352,494,000 | 41,903,576 | 0 | 0 | null | 1,441,352,210,000 | 1,441,352,210,000 | null | UTF-8 | Lean | false | false | 6,925 | hlean | /-
Copyright (c) 2015 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Floris van Doorn, Jakob von Raumer
-/
import .functor .iso
open eq category functor is_trunc equiv sigma.ops sigma is_equiv function pi funext iso
structure nat_trans {C D : Precateg... |
c2d5cd7f7334ac207891c417ff2e0640e15118cf | b73bd2854495d87ad5ce4f247cfcd6faa7e71c7e | /src/game/world2/level1.lean | 635ed9b63ca592ac8e4623fac8499d6ac376fe85 | [] | no_license | agusakov/category-theory-game | 20db0b26270e0c95a3d5605498570273d72f731d | 652dd7e90ae706643b2a597e2c938403653e167d | refs/heads/master | 1,669,201,216,310 | 1,595,740,057,000 | 1,595,740,057,000 | 280,895,295 | 12 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 951 | lean | import category_theory.category.default
import category_theory.isomorphism
universes v u -- The order in this declaration matters: v often needs to be explicitly specified while u often can be omitted
namespace category_theory
variables (C : Type u) [category.{v} C]
--rewrite this
/-
# Category world
## Level 1:... |
5ff23e6ca21a894d95c629a2d18d962c9bd1d163 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/linear_algebra/alternating.lean | 9a9988761210bb82e1cec8b290e97a0480e96318 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 42,987 | lean | /-
Copyright (c) 2020 Zhangir Azerbayev. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser, Zhangir Azerbayev
-/
import group_theory.group_action.quotient
import group_theory.perm.sign
import group_theory.perm.subgroup
import linear_algebra.linear_independent... |
744b5451c9af421e6e4babe29c45397bc957a3f9 | 08bd4ba4ca87dba1f09d2c96a26f5d65da81f4b4 | /doc/examples/widgets.lean | 56b98f43bc3bdf57d0a0936c0c8804ab8c1b492e | [
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"Apache-2.0",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | gebner/lean4 | d51c4922640a52a6f7426536ea669ef18a1d9af5 | 8cd9ce06843c9d42d6d6dc43d3e81e3b49dfc20f | refs/heads/master | 1,685,732,780,391 | 1,672,962,627,000 | 1,673,459,398,000 | 373,307,283 | 0 | 0 | Apache-2.0 | 1,691,316,730,000 | 1,622,669,271,000 | Lean | UTF-8 | Lean | false | false | 9,840 | lean | import Lean
open Lean Widget
/-!
# The user-widgets system
Proving and programming are inherently interactive tasks. Lots of mathematical objects and data
structures are visual in nature. *User widgets* let you associate custom interactive UIs with
sections of a Lean document. User widgets are rendered in the Lean in... |
6fe5fdcf6d7a1bf81729497fd7a5e8754d4037f9 | 54d7e71c3616d331b2ec3845d31deb08f3ff1dea | /tests/lean/macro_args.lean | 7532724c6c1d0a409695117379b2ae1946598f01 | [
"Apache-2.0"
] | permissive | pachugupta/lean | 6f3305c4292288311cc4ab4550060b17d49ffb1d | 0d02136a09ac4cf27b5c88361750e38e1f485a1a | refs/heads/master | 1,611,110,653,606 | 1,493,130,117,000 | 1,493,167,649,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 64 | lean | #eval ``({pos . line := zero, col := 1}).to_raw_expr.to_raw_fmt
|
9e36306a3158b1dcf9f6d00c293d10485c05e334 | cb1829c15cd3d28210f93507f96dfb1f56ec0128 | /theorem_proving/05-tactics.lean | e4ec00acf280dcf4139f40c71e9f7816004dfcdb | [] | no_license | williamdemeo/LEAN_wjd | 69f9f76e35092b89e4479a320be2fa3c18aed6fe | 13826c75c06ef435166a26a72e76fe984c15bad7 | refs/heads/master | 1,609,516,630,137 | 1,518,123,893,000 | 1,518,123,893,000 | 97,740,278 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 19,164 | lean | -- Chapter 5 Tactics
#print "=================================="
#print "Section 5.1"
#print " "
/- In this chapter, we describe an alternative approach to constructing proofs, using tactics.
A proof term is a representation of a mathematical proof; tactics are commands, or
instructions, that describe how to... |
075908803db49591c0f92ba60d601537fc5b0275 | 6432ea7a083ff6ba21ea17af9ee47b9c371760f7 | /tests/simpperf/pre1000.lean | 5ca18bacb574374e5858c07a45bb5d733671a9a4 | [
"Apache-2.0",
"LLVM-exception",
"NCSA",
"LGPL-3.0-only",
"LicenseRef-scancode-inner-net-2.0",
"BSD-3-Clause",
"LGPL-2.0-or-later",
"Spencer-94",
"LGPL-2.1-or-later",
"HPND",
"LicenseRef-scancode-pcre",
"ISC",
"LGPL-2.1-only",
"LicenseRef-scancode-other-permissive",
"SunPro",
"CMU-Mach"... | permissive | leanprover/lean4 | 4bdf9790294964627eb9be79f5e8f6157780b4cc | f1f9dc0f2f531af3312398999d8b8303fa5f096b | refs/heads/master | 1,693,360,665,786 | 1,693,350,868,000 | 1,693,350,868,000 | 129,571,436 | 2,827 | 311 | Apache-2.0 | 1,694,716,156,000 | 1,523,760,560,000 | Lean | UTF-8 | Lean | false | false | 84,532 | lean | axiom f (x : Prop) : Prop
axiom g0 (x : Prop) : Prop
axiom g1 (x : Prop) : Prop
axiom g2 (x : Prop) : Prop
axiom g3 (x : Prop) : Prop
axiom g4 (x : Prop) : Prop
axiom g5 (x : Prop) : Prop
axiom g6 (x : Prop) : Prop
axiom g7 (x : Prop) : Prop
axiom g8 (x : Prop) : Prop
axiom g9 (x : Prop) : Prop
axiom g10 (x : Prop) : P... |
3dab5dcc8e81a817fd5909c323fc2592619cba78 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/ring_theory/hahn_series.lean | e0e25df39dd3222464986fa5e33f20b8e4655058 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 61,736 | lean | /-
Copyright (c) 2021 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import order.well_founded_set
import algebra.big_operators.finprod
import ring_theory.valuation.basic
import ring_theory.power_series.basic
import data.finsupp.pwo
im... |
56d031e11e5280eb1b1bf9f0d281121db39c4b17 | fe208a542cea7b2d6d7ff79f94d535f6d11d814a | /src/Cantor/cantor.lean | d22f174952c2a43e690ac41f634041050b8d757b | [] | no_license | ImperialCollegeLondon/M1F_room_342_questions | c4b98b14113fe900a7f388762269305faff73e63 | 63de9a6ab9c27a433039dd5530bc9b10b1d227f7 | refs/heads/master | 1,585,807,312,561 | 1,545,232,972,000 | 1,545,232,972,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,324 | lean | -- Cantor's theorem in Lean
import tactic.interactive
open function
/- Theorem: If X is any type, then there is no bijective function f
from X to the power set of X.
-/
theorem no_bijection_to_power_set (X : Type) :
∀ f : X → set X, ¬ (bijective f) :=
begin
-- Proof by Kevin Buzzard
-- let f be an arbitrary... |
32172a87beb9343086189c2a6bee831c4c8e73c3 | 94e33a31faa76775069b071adea97e86e218a8ee | /src/analysis/locally_convex/with_seminorms.lean | bd06c9d3bd12ffcb45be4889f12cbf3d69610245 | [
"Apache-2.0"
] | permissive | urkud/mathlib | eab80095e1b9f1513bfb7f25b4fa82fa4fd02989 | 6379d39e6b5b279df9715f8011369a301b634e41 | refs/heads/master | 1,658,425,342,662 | 1,658,078,703,000 | 1,658,078,703,000 | 186,910,338 | 0 | 0 | Apache-2.0 | 1,568,512,083,000 | 1,557,958,709,000 | Lean | UTF-8 | Lean | false | false | 20,700 | lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Anatole Dedecker
-/
import analysis.seminorm
import analysis.locally_convex.bounded
/-!
# Topology induced by a family of seminorms
## Main definitions
* `seminorm_family... |
213aed7547cf115a3bab4a101819f247b0d18a1b | 07f5f86b00fed90a419ccda4298d8b795a68f657 | /library/init/data/int/order.lean | 1fb7bbc6ed1d7dfb2c43a95b35bbcd3b645b99a0 | [
"Apache-2.0"
] | permissive | VBaratham/lean | 8ec5c3167b4835cfbcd7f25e2173d61ad9416b3a | 450ca5834c1c35318e4b47d553bb9820c1b3eee7 | refs/heads/master | 1,629,649,471,814 | 1,512,060,373,000 | 1,512,060,469,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 11,806 | lean | /-
Copyright (c) 2016 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad
The order relation on the integers.
-/
prelude
import init.data.int.basic init.data.ordering.basic
namespace int
private def nonneg (a : ℤ) : Prop := int.cases_on a (as... |
e5f4167dda5d5dc94bc69561e28d58d02f70770e | 05f637fa14ac28031cb1ea92086a0f4eb23ff2b1 | /tests/lean/tst9.lean | ab7c8e5215e34a09eafa4e58d03c8387ba93574c | [
"Apache-2.0"
] | permissive | codyroux/lean0.1 | 1ce92751d664aacff0529e139083304a7bbc8a71 | 0dc6fb974aa85ed6f305a2f4b10a53a44ee5f0ef | refs/heads/master | 1,610,830,535,062 | 1,402,150,480,000 | 1,402,150,480,000 | 19,588,851 | 2 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 126 | lean | variable f : forall A : Type, A -> A -> A
variable N : Type
variable g : N -> N -> Bool
variable a : N
check g true (f _ a a)
|
e9c594ba3064eabbdbe425cba292ba2f062d030e | 05b503addd423dd68145d68b8cde5cd595d74365 | /src/topology/metric_space/emetric_space.lean | 3238c94c6826a0142ad09fc6f16d97130307aecf | [
"Apache-2.0"
] | permissive | aestriplex/mathlib | 77513ff2b176d74a3bec114f33b519069788811d | e2fa8b2b1b732d7c25119229e3cdfba8370cb00f | refs/heads/master | 1,621,969,960,692 | 1,586,279,279,000 | 1,586,279,279,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 40,305 | lean | /-
Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-/
import data.real.nnreal data.real.ennreal
import topology.uniform_space.separation topology.u... |
84f06dced1c25d6025d58c04c98b182773f8c086 | 50b3917f95cf9fe84639812ea0461b38f8f0dbe1 | /lean_together/Tues_talk/M1FQ1.lean | 08990c5677c05d357414a7d6ff4a0ab435fde825 | [] | no_license | roro47/xena | 6389bcd7dcf395656a2c85cfc90a4366e9b825bb | 237910190de38d6ff43694ffe3a9b68f79363e6c | refs/heads/master | 1,598,570,061,948 | 1,570,052,567,000 | 1,570,052,567,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 183 | lean | import data.real.basic
theorem M1F_sheet01_Q01a_is_F : ¬ (∀ x : ℝ, x ^ 2 - 3 * x + 2 = 0 → x = 1) :=
begin
intro H1,
have H2 := H1 2,
-- now I'm done, right?
sorry
end |
373a7a5f6851d15f8a1374937a63b38cb31cbd1e | 037dba89703a79cd4a4aec5e959818147f97635d | /src/2021/sets/sheet3.lean | 5f7ffb698d62ce3b1970a9f04122596e8279548f | [] | no_license | ImperialCollegeLondon/M40001_lean | 3a6a09298da395ab51bc220a535035d45bbe919b | 62a76fa92654c855af2b2fc2bef8e60acd16ccec | refs/heads/master | 1,666,750,403,259 | 1,665,771,117,000 | 1,665,771,117,000 | 209,141,835 | 115 | 12 | null | 1,640,270,596,000 | 1,568,749,174,000 | Lean | UTF-8 | Lean | false | false | 1,257 | lean | /-
Copyright (c) 2021 Kevin Buzzard. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author : Kevin Buzzard
-/
import tactic -- imports all the Lean tactics
/-!
# Sets in Lean, example sheet 3 : not in (`∉`)
The definition in Lean of `x ∉ A` is `¬ (x ∈ A)`. In other words,
`... |
7f565e612db09fe40ac4facdef86ac18420fd616 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/run/pred_using_structure_cmd.lean | 9216ebf0eda61dd63d1d44be96a8a20896264bc1 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 368 | lean | variable {A : Type}
structure has_refl (R : A → A → Prop) : Prop :=
(refl : ∀ a, R a a)
namespace test
structure is_equiv (R : A → A → Prop) extends has_refl R : Prop :=
(symm : ∀ a b, R a b → R b a)
(trans : ∀ a b c, R a b → R b c → R a c)
#check @has_refl.refl
#check @is_equiv.symm
#check @is_equiv.trans
#check @is... |
1c464e447ec7bd083a66a51fcae4cc6561bd3e17 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/group_theory/free_group.lean | 69a81c0839d860bdb97a0b3f6d2d97ee391ea9cf | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 27,817 | lean | /-
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau
Free groups as a quotient over the reduction relation `a * x * x⁻¹ * b = a * b`.
First we introduce the one step reduction relation
`free_group.red.step`: w * x * x⁻¹ * v ~... |
7f600d79abdf662d1e1b15cacfa201f4463e0ce6 | b328e8ebb2ba923140e5137c83f09fa59516b793 | /tests/lean/run/casesUsing.lean | 6c9b8f87a1333b03db531488a46ee120feb7429d | [
"Apache-2.0"
] | permissive | DrMaxis/lean4 | a781bcc095511687c56ab060e816fd948553e162 | 5a02c4facc0658aad627cfdcc3db203eac0cb544 | refs/heads/master | 1,677,051,517,055 | 1,611,876,226,000 | 1,611,876,226,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,226 | lean | import Lean
open Lean
open Lean.Meta
open Lean.Elab.Tactic
universes u
axiom elimEx (motive : Nat → Nat → Sort u) (x y : Nat)
(diag : (a : Nat) → motive a a)
(upper : (delta a : Nat) → motive a (a + delta.succ))
(lower : (delta a : Nat) → motive (a + delta.succ) a)
: motive y x
theorem ex1 (p q : Nat) : p ≤... |
d8735a8b08f76e28cd3eb60adf4a1151aef4e8ed | b7f22e51856f4989b970961f794f1c435f9b8f78 | /library/data/matrix.lean | b71de4fc67b0df8b6d2706885ee001f47a88f346 | [
"Apache-2.0"
] | permissive | soonhokong/lean | cb8aa01055ffe2af0fb99a16b4cda8463b882cd1 | 38607e3eb57f57f77c0ac114ad169e9e4262e24f | refs/heads/master | 1,611,187,284,081 | 1,450,766,737,000 | 1,476,122,547,000 | 11,513,992 | 2 | 0 | null | 1,401,763,102,000 | 1,374,182,235,000 | C++ | UTF-8 | Lean | false | false | 3,236 | lean | /-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
Matrices
-/
import algebra.ring data.fin data.fintype
open fin nat
definition matrix [reducible] (A : Type) (m n : nat) := fin m → fin n → A
namespace matrix... |
8e55741c7e3e83a7318a9dde8a6607fe71e54d26 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/category_theory/adjunction/lifting.lean | 3e0e6f4f13914759e417143d783a3f1a88b6d514 | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 11,871 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import category_theory.limits.shapes.equalizers
import category_theory.limits.shapes.reflexive
import category_theory.adjunction
import category_theory.monad.adjunction
i... |
7c9b312d62d8d6d3c5b30bdbd84ecea1d1ef36cc | 690889011852559ee5ac4dfea77092de8c832e7e | /test/tactics.lean | 182669f7c564e2144566b590cfba867a23bc03bf | [
"Apache-2.0"
] | permissive | williamdemeo/mathlib | f6df180148f8acc91de9ba5e558976ab40a872c7 | 1fa03c29f9f273203bbffb79d10d31f696b3d317 | refs/heads/master | 1,584,785,260,929 | 1,572,195,914,000 | 1,572,195,913,000 | 138,435,193 | 0 | 0 | Apache-2.0 | 1,529,789,739,000 | 1,529,789,739,000 | null | UTF-8 | Lean | false | false | 10,410 | lean | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon, Scott Morrison
-/
import tactic.interactive tactic.finish tactic.ext tactic.lift tactic.apply tactic.reassoc_axiom
example (m n p q : nat) (h : m + n = p) : true :=
begin
... |
f3bf6fee5e89b1334e594c4f5844ecff9644d5cc | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /src/data/complex/module.lean | cac447e5921fc2846915034a2928325287242924 | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 16,838 | lean | /-
Copyright (c) 2020 Alexander Bentkamp, Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Bentkamp, Sébastien Gouëzel, Eric Wieser
-/
import algebra.order.smul
import data.complex.basic
import data.fin.vec_notation
import field_theory.tower
... |
e7c803b7b81288359654715d3fddb39725f6aca0 | 8cae430f0a71442d02dbb1cbb14073b31048e4b0 | /test/lift.lean | b48d2b0a69e93bbb2155f26d08f2f3905e85c3aa | [
"Apache-2.0"
] | permissive | leanprover-community/mathlib | 56a2cadd17ac88caf4ece0a775932fa26327ba0e | 442a83d738cb208d3600056c489be16900ba701d | refs/heads/master | 1,693,584,102,358 | 1,693,471,902,000 | 1,693,471,902,000 | 97,922,418 | 1,595 | 352 | Apache-2.0 | 1,694,693,445,000 | 1,500,624,130,000 | Lean | UTF-8 | Lean | false | false | 3,508 | lean | import data.set.basic
import tactic.lift
/-! Some tests of the `lift` tactic. -/
example (n m k x z u : ℤ) (hn : 0 < n) (hk : 0 ≤ k + n) (hu : 0 ≤ u)
(h : k + n = 2 + x) (f : false) :
k + n = m + x :=
begin
lift n to ℕ using le_of_lt hn,
guard_target (k + ↑n = m + x), guard_hyp hn : (0 : ℤ) < ↑n,
lift m to... |
bd0bf85ffa0addd05c537ad49b0c3b84f68b2888 | cf39355caa609c0f33405126beee2739aa3cb77e | /tests/lean/assumption_tac_notation.lean | 228257ba93096bc9890eb57025e3057caec43043 | [
"Apache-2.0"
] | permissive | leanprover-community/lean | 12b87f69d92e614daea8bcc9d4de9a9ace089d0e | cce7990ea86a78bdb383e38ed7f9b5ba93c60ce0 | refs/heads/master | 1,687,508,156,644 | 1,684,951,104,000 | 1,684,951,104,000 | 169,960,991 | 457 | 107 | Apache-2.0 | 1,686,744,372,000 | 1,549,790,268,000 | C++ | UTF-8 | Lean | false | false | 144 | lean | example (A : Type) (a : A) : A := ‹A›
example (A : Type) (a : A) := ‹A›
example (A : Type) : A := ‹A›
example (A : Type) := ‹A›
|
8531e34362bb8cdb79e998a415944d7d66312f53 | 618003631150032a5676f229d13a079ac875ff77 | /src/topology/instances/nnreal.lean | 975e9f200b9a12916b050848892051b5447e674e | [
"Apache-2.0"
] | permissive | awainverse/mathlib | 939b68c8486df66cfda64d327ad3d9165248c777 | ea76bd8f3ca0a8bf0a166a06a475b10663dec44a | refs/heads/master | 1,659,592,962,036 | 1,590,987,592,000 | 1,590,987,592,000 | 268,436,019 | 1 | 0 | Apache-2.0 | 1,590,990,500,000 | 1,590,990,500,000 | null | UTF-8 | Lean | false | false | 4,655 | lean | /-
Copyright (c) 2018 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
Nonnegative real numbers.
-/
import topology.algebra.infinite_sum
noncomputable theory
open set topological_space metric
open_locale topological_space
namespace nnreal... |
b5516fc292fe4eb674367ec3b34624ec1b9bacf7 | 74addaa0e41490cbaf2abd313a764c96df57b05d | /Mathlib/category_theory/subterminal_auto.lean | d755a6721deea2ca74ab83f1f7a8fcb2c3a40906 | [] | no_license | AurelienSaue/Mathlib4_auto | f538cfd0980f65a6361eadea39e6fc639e9dae14 | 590df64109b08190abe22358fabc3eae000943f2 | refs/heads/master | 1,683,906,849,776 | 1,622,564,669,000 | 1,622,564,669,000 | 371,723,747 | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 5,804 | lean | /-
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
import Mathlib.PrePort
import Mathlib.Lean3Lib.init.default
import Mathlib.category_theory.limits.shapes.terminal
import Mathlib.category_theory.limits.shapes.binary_prod... |
362d8ad6af1162b53e49fae48715ff24041a5312 | 7cef822f3b952965621309e88eadf618da0c8ae9 | /src/measure_theory/l1_space.lean | d321d657709460d8666362b3737841ac181a2963 | [
"Apache-2.0"
] | permissive | rmitta/mathlib | 8d90aee30b4db2b013e01f62c33f297d7e64a43d | 883d974b608845bad30ae19e27e33c285200bf84 | refs/heads/master | 1,585,776,832,544 | 1,576,874,096,000 | 1,576,874,096,000 | 153,663,165 | 0 | 2 | Apache-2.0 | 1,544,806,490,000 | 1,539,884,365,000 | Lean | UTF-8 | Lean | false | false | 27,453 | lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou
-/
import measure_theory.ae_eq_fun
/-!
# Integrable functions and `L¹` space
In the first part of this file, the predicate `integrable` is defined and basic properties ... |
8246024840db5bead5f12c246606f7ee212fb646 | aa3f8992ef7806974bc1ffd468baa0c79f4d6643 | /tests/lean/run/elab_bug1.lean | dcbd68d8847c6377f47c4ea9746f8e3279bee05b | [
"Apache-2.0"
] | permissive | codyroux/lean | 7f8dff750722c5382bdd0a9a9275dc4bb2c58dd3 | 0cca265db19f7296531e339192e9b9bae4a31f8b | refs/heads/master | 1,610,909,964,159 | 1,407,084,399,000 | 1,416,857,075,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 2,791 | lean | ----------------------------------------------------------------------------------------------------
--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
--- Released under Apache 2.0 license as described in the file LICENSE.
--- Author: Jeremy Avigad
------------------------------------------------------... |
0f7d9b41aa94340cdad7914a67e91708b67f26f0 | d9d511f37a523cd7659d6f573f990e2a0af93c6f | /src/group_theory/group_action/units.lean | 02384a5f0538bc9a2c1da9bd09bd5139836c340a | [
"Apache-2.0"
] | permissive | hikari0108/mathlib | b7ea2b7350497ab1a0b87a09d093ecc025a50dfa | a9e7d333b0cfd45f13a20f7b96b7d52e19fa2901 | refs/heads/master | 1,690,483,608,260 | 1,631,541,580,000 | 1,631,541,580,000 | null | 0 | 0 | null | null | null | null | UTF-8 | Lean | false | false | 4,915 | lean | /-
Copyright (c) 2021 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import group_theory.group_action.defs
/-! # Group actions on and by `units M`
This file provides the action of a unit on a type `α`, `has_scalar (units M) α`, in the pres... |
e9c115a2dd8f69c321b30de08163ecbb1de98305 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/topology/category/Top/epi_mono.lean | c99937ab9c3bc766b56c4fc0ee1a39157eda2b8c | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 1,189 | lean | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Reid Barton
-/
import topology.category.Top.adjunctions
import category_theory.epi_mono
/-!
# Epi- and monomorphisms in `Top`
This file shows that a continuous function is an epimorphis... |
7886638cd2da0df4102cae4f979eff4021cce2d6 | fa02ed5a3c9c0adee3c26887a16855e7841c668b | /src/data/multiset/finset_ops.lean | 74b0f7f68652be7100968fca1277f5bd8236e60d | [
"Apache-2.0"
] | permissive | jjgarzella/mathlib | 96a345378c4e0bf26cf604aed84f90329e4896a2 | 395d8716c3ad03747059d482090e2bb97db612c8 | refs/heads/master | 1,686,480,124,379 | 1,625,163,323,000 | 1,625,163,323,000 | 281,190,421 | 2 | 0 | Apache-2.0 | 1,595,268,170,000 | 1,595,268,169,000 | null | UTF-8 | Lean | false | false | 8,764 | lean | /-
Copyright (c) 2017 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
import data.multiset.erase_dup
/-!
# Preparations for defining operations on `finset`.
The operations here ignore multiplicities,
and preparatory for defining the c... |
1ee96c75f8a17ffe904018d2b8fca04a3f453952 | 4727251e0cd73359b15b664c3170e5d754078599 | /src/data/nat/choose/cast.lean | 935edef67ccf48330d0c95a41915cc581c0e6006 | [
"Apache-2.0"
] | permissive | Vierkantor/mathlib | 0ea59ac32a3a43c93c44d70f441c4ee810ccceca | 83bc3b9ce9b13910b57bda6b56222495ebd31c2f | refs/heads/master | 1,658,323,012,449 | 1,652,256,003,000 | 1,652,256,003,000 | 209,296,341 | 0 | 1 | Apache-2.0 | 1,568,807,655,000 | 1,568,807,655,000 | null | UTF-8 | Lean | false | false | 1,490 | lean | /-
Copyright (c) 2021 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.nat.choose.basic
import data.nat.factorial.cast
/-!
# Cast of binomial coefficients
This file allows calculating the binomial coefficient `a.choose b` as an... |
30486eeb960d07c8736e28f016bb2735c1700394 | 367134ba5a65885e863bdc4507601606690974c1 | /src/category_theory/abelian/pseudoelements.lean | 7e212f454e32bdffa3d7b0d15b8ec25097a5534c | [
"Apache-2.0"
] | permissive | kodyvajjha/mathlib | 9bead00e90f68269a313f45f5561766cfd8d5cad | b98af5dd79e13a38d84438b850a2e8858ec21284 | refs/heads/master | 1,624,350,366,310 | 1,615,563,062,000 | 1,615,563,062,000 | 162,666,963 | 0 | 0 | Apache-2.0 | 1,545,367,651,000 | 1,545,367,651,000 | null | UTF-8 | Lean | false | false | 18,841 | lean | /-
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
import category_theory.abelian.exact
import category_theory.over
/-!
# Pseudoelements in abelian categories
A *pseudoelement* of an object `X` in an abelian category ... |
8af654cee1b8e2350cd47c5a783d6e58f848aa70 | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /stage0/src/Lean/MonadEnv.lean | c727074d6421e2e6d62ffecd74a19834f9d42772 | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 6,921 | lean | /-
Copyright (c) 2020 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
import Lean.Environment
import Lean.Exception
import Lean.Declaration
import Lean.Util.FindExpr
import Lean.AuxRecursor
namespace Lean
def setEnv [MonadEn... |
3af2be862430c3998bfc158f8556591393f611f8 | 9dc8cecdf3c4634764a18254e94d43da07142918 | /src/measure_theory/function/conditional_expectation/basic.lean | b122f9e743a4ccaa4fc3e256aebb5f6bb96fc792 | [
"Apache-2.0"
] | permissive | jcommelin/mathlib | d8456447c36c176e14d96d9e76f39841f69d2d9b | ee8279351a2e434c2852345c51b728d22af5a156 | refs/heads/master | 1,664,782,136,488 | 1,663,638,983,000 | 1,663,638,983,000 | 132,563,656 | 0 | 0 | Apache-2.0 | 1,663,599,929,000 | 1,525,760,539,000 | Lean | UTF-8 | Lean | false | false | 109,079 | lean | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
import analysis.inner_product_space.projection
import measure_theory.function.l2_space
import measure_theory.decomposition.radon_nikodym
import measure_theory.function.u... |
675be20c0ffa6b83722b344050c8df14b4e3827d | 57aec6ee746bc7e3a3dd5e767e53bd95beb82f6d | /stage0/src/Lean/Data/Lsp/Ipc.lean | 7469cf43cf2b1020bd89a6096531d67b5145e9af | [
"Apache-2.0"
] | permissive | collares/lean4 | 861a9269c4592bce49b71059e232ff0bfe4594cc | 52a4f535d853a2c7c7eea5fee8a4fa04c682c1ee | refs/heads/master | 1,691,419,031,324 | 1,618,678,138,000 | 1,618,678,138,000 | 358,989,750 | 0 | 0 | Apache-2.0 | 1,618,696,333,000 | 1,618,696,333,000 | null | UTF-8 | Lean | false | false | 2,628 | lean | /-
Copyright (c) 2020 Marc Huisinga. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Marc Huisinga, Wojciech Nawrocki
-/
import Init.System.IO
import Lean.Data.Json
import Lean.Data.Lsp.Communication
import Lean.Data.Lsp.Diagnostics
import Lean.Data.Lsp.Extra
/-! Prov... |
dda80b2bfa11d5988c5b43860035182b0ea7404c | c777c32c8e484e195053731103c5e52af26a25d1 | /src/model_theory/types.lean | 2df5368d2a6f2cd07d2acb84087d6d42df0e4a6d | [
"Apache-2.0"
] | permissive | kbuzzard/mathlib | 2ff9e85dfe2a46f4b291927f983afec17e946eb8 | 58537299e922f9c77df76cb613910914a479c1f7 | refs/heads/master | 1,685,313,702,744 | 1,683,974,212,000 | 1,683,974,212,000 | 128,185,277 | 1 | 0 | null | 1,522,920,600,000 | 1,522,920,600,000 | null | UTF-8 | Lean | false | false | 7,634 | lean | /-
Copyright (c) 2022 Aaron Anderson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Aaron Anderson
-/
import model_theory.satisfiability
/-!
# Type Spaces
This file defines the space of complete types over a first-order theory.
(Note that types in model theory are di... |
725695babe01b3ce713b8f5d77c230cede639c70 | a45212b1526d532e6e83c44ddca6a05795113ddc | /src/data/list/alist.lean | 2e081706e7941095c90a34ddd2ddc624934a6509 | [
"Apache-2.0"
] | permissive | fpvandoorn/mathlib | b21ab4068db079cbb8590b58fda9cc4bc1f35df4 | b3433a51ea8bc07c4159c1073838fc0ee9b8f227 | refs/heads/master | 1,624,791,089,608 | 1,556,715,231,000 | 1,556,715,231,000 | 165,722,980 | 5 | 0 | Apache-2.0 | 1,552,657,455,000 | 1,547,494,646,000 | Lean | UTF-8 | Lean | false | false | 8,089 | lean | /-
Copyright (c) 2018 Sean Leather. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sean Leather, Mario Carneiro
Association lists.
-/
import data.list.sigma
universes u v w
open list
variables {α : Type u} {β : α → Type v}
/-- `alist β` is a key-value map stored as ... |
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